"Lagrangian" for a Non-Lagrangian Field Theory with N=2 Supersymmetry.

We suggest that at least some of the strongly coupled N=2 quantum field theories in 4D can have a nonconformal N=1 Lagrangian description flowing to them at low energies. In particular, we construct such a description for the N=2 rank one superconformal field theory with E(6) flavor symmetry, for which a Lagrangian description was previously unavailable. We utilize this description to compute several supersymmetric partition functions.

Four dimensional superconformal index from q-deformed two dimensional Yang-Mills theory.

We show that the superconformal index (the partition function on the three-sphere times a circle) of a certain class of 4D supersymmetric field theories is exactly equal to a partition function of q-deformed nonsupersymmetric 2D Yang-Mills theory.